A rectangular painting's width is 6 less than twice its length.

Find the quotient (line over 42 is repeating)

strojnjashka [21]

The correct answer is: [C]:  " $\frac{21}{11}$ " .
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<span>Explanation:
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</span>
Let us begin by converting the:
"0.42 (with the "repeating bar on the digits, "42") " ;

into a fraction, as follows:
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Let x = 0.42424242424242424242424242424242....

100x = 42.42424242424242424242424242424242....
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100x = 42.42424242424242424242424242424242....
– x = 0.42424242424242424242424242424242...
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99x = 42.000000000000000000000000000000.... ;

→ 99x = 42 ;

Divide each side of the equation by " 99 " ;
to isolate "x" on one side of the equation; & to solve for "x" ;
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→ 99x / 99 = 42/99 = (42 ÷ 3) / (99 ÷ 3) = 14/ 33;

→ x = " $\frac{14}{33}$ " .

So; "0.42 (with a repeating bar over the digits, "42" ;

is equal to: " $\frac{14}{33}$ "
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So, rewrite the question/problem being asked:
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"Find the quotient:
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$\frac{14}{33}$ ÷ $\frac{2}{9}$ ;

=   $\frac{14}{33}$ * $\frac{9}{2}$ ;

Note: The "14" cancels to a "7" <span>; and</span> the "2" cancels to a "1" ;
→ {since: " 14 ÷ 2 = 7 " ; and since: " 2 ÷ 2 = 1 "} ;

Note : The "33" cancels to an "11" ; and the "9" cancels to a "3" ;
   → {since: " 33 ÷ 3 = 11 " ; and since: " 9 ÷ 3 = 3 "} ;

And we can rewrite the problem as:
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" $\frac{7}{11}$ * $\frac{3}{1}$ " ;

= $\frac{(7*3)}{(11*1}$ = $\frac{21}{11}$ ;

→ which is: Answer choice: [C]: " $\frac{21}{11}$ " .
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3 0

4 years ago

Kayla knows that 1/16

Anastasy [175]

Answer:

The quotient is 0. 0625 and the empty boxes in remainder are 4 and 8 respectively

Step-by-step explanation:

Given: $\frac{1}{16}$ or 1 divided by 16

Step 1: dividend is 1 and divisor 16 it is not divisible by 16 so the Quotient is 0 remainder is 1 .

Step 2: taking the decimal point above now dividend is 10 and divisor is 16 so it is again not divisible by 16 so the quotient is 0.0 and remainder is 10 now bringing next 0 in remainder so the dividend becomes 100.

Step 3: now dividend is 100 and divisor is 16 which is divisible by 16 by 6 times which is 96 so the Quotient becomes 0.06 and remainder becomes 4 now bringing next 0 in remainder so the dividend becomes 40.

Step 4: now dividend is 40 and divisor is 16 which is divisible by 16 by 2 times which is 32 so the Quotient becomes 0.062 and remainder becomes 8 now bringing next 0 in remainder so the dividend becomes 80.

Step 5: now dividend is 80 and divisor is 16 which is divisible by 16 by 5 times which is 80 so the Quotient becomes 0.0625 and remainder becomes 0